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Like Bono, I’m singing “We’re one, but we’re not the same”

Today, the threat of an NHL lockout draws nearer. The league and its players have a pile of money and little regard for their customers. Kinda like these two:

Lockout or not, it is that time of year. Some hockey talk:

Well it’s too late tonightTo drag the past out into the light

In 2003, the Vancouver Canucks faced the Dallas Stars in the first round of the Stanley Cup playoffs. Canucks fans may remember the opening game of this series as the one in which Henrik Sedin scored the game-winning goal late in the fourth overtime period. They may also remember it as the most boring playoff series ever. Considering the series went 7 games and 3 games went to overtime, this was no easy feat. In the middle of the series, the final scores were 0-2, 2-1, 2-1, and 1-0. During this stretch, the colour commentator said something like “Turco has a save percentage of 0.960, but he’s gotta be frustrated because the guy at the other end [Luongo] is playing twice as good”. Luongo’s save percentage was 0.980¹.

This floored me. How can that be? We’re talking about a difference of only 2 percentage points. He must have made a mistake. Twice as good?

The answer lies in part-part-whole relationships. What if we focussed on the other part in this part-part-whole relationship, the goals against?

What if, rather than save percentages, goalies’ goals against percentages were discussed? Let’s abbreviate this as a goalie’s GAP. Heh. Seems fitting:

Turco’s GAP would be 0.040; Luongo’s 0.020. Yep. Harry Neale was right. A GAP of 0.020 is twice as good as a GAP of 0.040 since 0.020 × 2 = 0.040. Still, we’re talking about a difference of only 2 percentage points.

Is it getting better?Or do you feel the same?

But wait. GAP is a unit rate. We’ve been talking about unit rates on this blog. Luongo’s GAP of 0.020 means 0.020 goals per one shot against (or 20 goals per 1000 shots against). This can also be expressed as one goal per 50 shots against (1/0.020 = 50). Turco’s GAP of 0.040, on the other hand (the left one), means 0.040 goals per one shot against. This can be expressed as one goal per 25 shots against. Let’s call this a goalie’s Shots Against per Goal, or SAG. Fifty versus 25 seems like a much bigger difference than 98 versus 96. Just visualize the bar graphs.

Did I disappoint you?Or leave a bad taste in your mouth?

In Vancouver, the goalie controversy is proceeding to its logical conclusion.

What a fun post Chris! I love discussions about the importance of the idea of “what ‘one’ is”. Not to mention, weaving in an awesome rock band and my favourite (team) sport.
I’ve noticed far too many people (adults included) don’t recognize how important the concept of “the unit” is and it’s impact on arguments. It’s always great to see examples of how to engage more people in those conversations. Thanks!

An interesting graph would be a shot number on the x-axis, and save percentage on the y-axis. You could see big jumps (3/3 saves => 100% save rate go to 3/4 saves => 75% saverste after a goal) and how the goalies save % climbs back up after each save.

Great idea, Dan. Hopefully there will be an NHL season this year so that I can collect some data. Wait a sec! You’re a hockey coach, aren’t you?

I was also thinking about goals against averages in terms of unit rates. Here the unit is one game. But not all games are considered equal. In the first game of that Canucks vs. Stars series mentioned above, Roberto Luongo was named First Star (in his first playoff appearance) despite having let in 4 goals. He also made 72 saves. This is why hockey fans also look at a goalie’s Sv%. As you know, one game is defined as 60 minutes. The winning goal was scored 18 minutes into the 4th overtime period. Luongo’s career playoff GAA at this point in the series would have been 4 divided by 138/60, or 1.74. It now sits at 2.52. It’s got to be much higher than that against the ‘Hawks.

I think it’s also especially interesting to look at a goalie’s GAA when he gets pulled. Let’s say a goalie lets in 3 goals in the first 5 minutes on the opening night of the NHL season before getting the hook. His GAA is 3 / 1/12 = 36.00. If he remains in the game without letting in another goal, his GAA is 3.00. Either way, he let in 3 goals. It’s about “What is 1?”